What your neighbor is doing is wrong; she isn’t trying to help anyone, but is only interested in building herself up by tearing other people down. The Bible is clear: “Do not let any unwholesome talk come out of your mouths, but only what is helpful for building others up according to their needs” (Ephesians 4:29).
But I suspect your neighbor is wrong also because much of what she says probably isn’t true (or at least it isn’t the full story). This is one reason why the Bible condemns gossip and warns us not to make it part of our lives. Gossip always creates suspicion, and even if it’s true, it always causes conflict and division. In addition, no one who practices gossip does so out of pure motives or a sincere love for others. The Bible rightly says, “A perverse person stirs up conflict, and a gossip separates close friends” (Proverbs 16:28).
What can you do? First, make sure that you don’t fall into the same habits as your neighbor. If you can’t say something good about someone, leave it unsaid. Then ask God to give you an opportunity to challenge your neighbor. If she brings up something bad about someone, ask if she knows anything good about them. Then gently but firmly let her know that you don’t want gossip to be part of your life, and you hope she’ll do the same. Most of all, pray that she’ll open her heart and life to Jesus Christ and His life-changing love.